A sample of a radioactive substance decayed to 96% of its original amount after
ID: 2877462 • Letter: A
Question
A sample of a radioactive substance decayed to 96% of its original amount after a year. (Round your answers to two decimal places.) A) What is the half-life of the substance? B) How long would it take the sample to decay to 90% of its original amount? A sample of a radioactive substance decayed to 96% of its original amount after a year. (Round your answers to two decimal places.) A) What is the half-life of the substance? B) How long would it take the sample to decay to 90% of its original amount? A) What is the half-life of the substance? B) How long would it take the sample to decay to 90% of its original amount?Explanation / Answer
(A) Let the decay model be A(t) = A(0) e^(-kt)
A(t)/A(0) = e^(-kt)
0.96 = e^-k
ln 0.96 = -k
k = 0.0408
So, the model is A(t) = A(0) * e^(-0.0408t)
At half life, A(t)/A(0) = 0.5
0.5 = e^(-0.0408t)
ln 0.5 = -0.0408t
t = ln 0.5 / -0.0408 = 16.98
Half life = 16.98 years
(B)Here, A(t)/A(0) = 0.90
0.90 = e^(-0.0408t)
ln 0.9 = -0.0408t
t = ln 0.9 / -0.0408 = 2.58 years.